Non-archimedean stratifications in power bounded T-convex fields

2017/04/21 by Erick García Ramírez, Ramírez, Erick García
Mathematics · #03C64 #03C98 #14P99 #Advanced Differential Equations and Dynamical Systems #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1704.06558

openalex publication_date 2017/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that functions definable in power bounded T-convex fields have the (multidimensional) Jacobian property. Building on work of I. Halupczok, this implies that a certain notion of non-archimedean stratifications is available in such valued fields. From the existence of these stratifications, we derive some applications in an archimedean o-minimal setting. As a minor result, we also show that if T is power bounded, the theory of T-convex valued fields is b-minimal with centres.

Citations

• Quantifier elimination and minimality conditions in algebraically closed valued fields
• Geometric categories and o-minimal structures

Related

• Lipschitz stratifications in power-bounded o-minimal fields
• A Non-Archimedean Approach to Stratifications
• Integration in power-bounded T-convex valued fields
• Restricted analytic valued fields with partial exponentiation
• Generalized Euler characteristic in power-bounded T-convex valued fields